Perictione (Περικτιόνη) was the mother of the philosopher Plato and a philosopher in her own right — descended through Solon and Critias from the kings of Athens. A treatise on the harmony of women (Peri gynaikos harmonias) and fragments on the duties of women are attributed to a Perictione (possibly her, possibly a later Pythagorean of the same name).
Perictione does not currently appear in the US Social Security Administration's top 1,000 girls' names, so we don't publish a US rank or birth count for it. That says nothing about the name's standing elsewhere in the world — only that it sits outside the ranked US data we rely on.
In Pythagorean numerology the letters of Perictione reduce to 6, The Nurturer. This is a traditional interpretive system, not a factual claim about the name.